We describe how to obtain bounds on the spectrum of a non-self-adjoint operator by means of what we call its higher order numerical ranges. We prove some of their basic properties and describe explain how to compute them. We finally use them to obtain new spectral insights into the non-selfadjoint Anderson model in one and two space dimensions. keywords: non-self-adjoint operator, spectrum, num...

We present an operator approach to Rogers-type formulas and Mehler’s formulas for the Al-Salam-Carlitz polynomials Un(x, y, a; q). By using the q-exponential operator, we obtain a Rogers-type formula which leads to a linearization formula. With the aid of a bivariate augmentation operator, we get a simple derivation of Mehler’s formula due to AlSalam and Carlitz. By means of the Cauchy companio...

An operator is defined that is analogous to the time translation operator except that it translates every component of a state in energy by an amount ε. A prescription for measuring expectation values of this operator is described. These measurements provide phase information that is not obtainable by other means. The similarity of this treatment with the treatment of reccurrence spectroscopy i...

Background: Heat stress in the steel industry is considered as a serious threat to the health and safety of workers. A wide spectrum of complications and diseases from mild disorders such as burning sensation to fatal conditions such as thermal shock may occur due to uncontrolled thermal stress. In this study, heat stress assessment was performed according to the wet-bulb globe temperature (WBG...